WJEC GCSE Mathematics Unit 2: Calculator-allowed Higher November 2022 question paper 3300U60-1

A solid metal cylinder has a radius of 2∙3 cm and a height of 5 cm.

The mass of the cylinder is 423·1 g.

Find the density of the metal.

Give your answer in g/cm³.

A rectangle has a width of 4x 10.

The perimeter of the rectangle is 14x 4.

Find the length of the rectangle in terms of x.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A, B and C are points on the circumference of a circle with centre O. The length of BC is 10 cm. The diameter of the circle is 18 cm.

Calculate the shaded area.

You must show all your working.

Calculate the length of the side YZ in the triangle XYZ shown below.

Two times are recorded correct to the nearest 0·1 second.

Calculate the greatest possible difference between these times.

A number has been increased by 60% to give an answer of 64.

What was the original number?

Bag A and Bag B contain only red and blue balls.

The probability of choosing a red ball from Bag A is . The probability of choosing a red ball from Bag B is 0∙25.

A ball is chosen at random from each bag.

Complete the tree diagram below.

Find the probability that the two balls chosen are the same colour.

Expand and simplify 2h 3t5h 7t.

A cone is joined to a hemisphere, as shown below. The cone has a base radius of 8 cm and a slant height of 17 cm. The hemisphere has the same radius as the cone.

Calculate the surface area of the composite solid.

Two similar shapes have perimeters of 241 cm and 719 cm. The area of the smaller shape is 2063 cm².

Calculate the area of the larger shape.

Give your answer in m².

DE is the tangent to the circle at point A, as shown below.

BC = 7 cm and AC = 13 cm. BAD = 68° and CAE = 80°.

Calculate the area of the triangle ABC.

Write down an irrational number whose value is between 9 and 10.

Write your answer in the box below.

Fully factorise the expression k³p – kp³.

The following nine cards are placed in a box.

Catherine chooses three cards at random from the box, without replacement.

Calculate the probability that the three cards drawn show the letters ‘A’, ‘F’ and ‘O’ in

that order.

Calculate the probability that two of the three cards show the same letter.

Make c the subject of the following formula.

The diagram shows a triangle ABC and a circle with centre C. The points B and D lie on the circumference of the circle.

The length of the line AB is 19 cm. The length of the line AC is 29 cm. The radius of the circle is xcm.

Calculate the area of the shaded sector BCD.